On Prediction in Science

In order to bring into proper focus the significance of correct prediction
in science, I offer at the start a short survey of the most celebrated
cases, and it is not by chance that almost all of them come from the domain
of astronomy. These cases are spectacular and, with one or two exceptions,
are well known.

The story of scientific “clairvoyance” in modern astronomy starts with
Johannes Kepler, a strange case and little known. When Galileo, using
the telescope he had built after the model of an instrument invented by
a Danish craftsman, discovered the satellites circling Jupiter, Kepler
became very eager to see the satellites himself and begged in letters
to have an instrument sent to Prague; Galileo did not even answer him.
Next, Galileo made two more discoveries, but before publishing them in
a book, he assured himself of priority by composing cryptograms, not an
uncommon procedure in those days: statements written in Latin were deliberately
reduced to the letters of which the sentences were composed, or, if the
author of the cryptogram so wished, the letters were re-assembled to make
a different sentence. The second way was chosen by Galileo when he thought
he had discovered that Saturn is “a triple” planet, having observed appendices
on both sides of Saturn, but not having discerned that they were but a
ring around the planet, a discovery reserved for Christian Huygens in
1659, half a century later. Kepler tried to read the cryptogram of letters
recombined into a non-revealing sentence, but did not succeed. He offered
as his solution: “Salute, fiery twin, offspring of Mars” (“Salve, umbistineum
geminatum Martia proles” ). Of this, Arthur Koestler in The Sleepwalkers
(1959) wrote (p. 377): “He [Kepler] accordingly believed that Galileo
had discovered two moons around Mars.” But Galileo did not discover them
and they remained undiscovered for more than two hundred fifty years.
Strangely, Koestler passes over the incident without expressing wonder
at Kepler’s seeming prescience.

As I have shown in Worlds in Collision (“The Steeds of Mars” )
the poets Homer and Virgil knew of the trabants of Mars, visualized as
his steeds, named Deimos (Terror) and Phobos (Rout). Kepler referred to
the satellites of Mars as being “burning” or “flaming” , the same way
the ancients had referred to the steeds of Mars.

Ancient lore preserved traditions from the time when Mars, Ares of the
Greeks, was followed and preceded by swiftly circling satellites with
their blazing manes. “When Mars was very close to the earth, its two trabants
were visible. They rushed in front of and around Mars; in the disturbances
that took place, they probably snatched some of Mars’ atmosphere, dispersed
as it was, and appeared with gleaming manes” (Worlds in Collision,
p. 230).

Next, Galileo made the discovery that Venus shows phases, as the Moon
does. This time he secured his secret by locking it in a cryptogram of
a mere collection of letters—so many A’s, so many B’s, and so on. Kepler
again tried to read the cryptogram and came up with the sentence: “Macula
rufa in Jove est gyratur mathem etc.” which in translation reads: “There
is a red spot in Jupiter which rotates mathematically.”

The wondrous thing is: how could Kepler have known of the red spot in
Jupiter, then not yet discovered? It was discovered by J. D. Cassini in
the 1660’s, after the time of Kepler and Galileo. Kepler’s assumption
that Galileo had discovered a red spot in Jupiter amazes and defies every
statistical chance of being a mere guess. But the possibility is not excluded
that Kepler found the information in some Arab author or some other source,
possibly of Babylonian or Chinese origin. Kepler did not disclose what
the basis of his reference to the red spot of Jupiter was — he could not
have arrived at it either by logic and deduction or by sheer guesswork.
A scientific prediction must follow from a theory as a logical consequence.
Kepler had no theory on that. It is asserted that the Chinese observed
solar spots many centuries before Galileo did with his telescope. Observing
solar spots, the ancients could have conceivably observed the Jovian red
spot, too. Jesuit scholars traveled in the early 17th century to China
to study Chinese achievements in astronomy.

Kepler was well versed in ancient writings, also knowledgeable in medieval
Arab authors; for instance, he quoted Arzachel to support the view that
in ancient times Babylon must have been situated two and a half degrees
more to the north, and this on the basis of the data on the duration of
the longest and shortest days in the year as registered in ancient Babylon.1

Jonathan Swift, in his Gulliver’s Travels (1726) tells of the
astronomers of the imaginary land of the Laputans who asserted they had
discovered that the planet Mars has “two lesser stars, or satellites,
which revolve about Mars, whereof the innermost is distant from the center
of the primary planet exactly three of [its] diameters, and the outermost
Five; the former revolves in the space of ten hours, and the latter in
twenty-one-and-a-half; so that the squares of their periodical times are
very near in the same proportion with the cubes of their distance from
the center of Mars, which evidently shows them to be governed by the same
law of gravitation that influences the other heavenly bodies.”

About this passage a literature of no mean number of authors grew in
the years after 1877, when Asaph Hall, a New England carpenter turned
astronomer, discovered the two trabants of Mars. They are between five
and ten miles in diameter. They revolve on orbits close to their primary
and in very short times: actually the inner one, Phobos, makes more than
three revolutions in the time it takes Mars to complete one rotation on
its axis; and were there intelligent beings on Mars they would need to
count two different months according to the number of satellites (this
is no special case — Jupiter has twelve moons and Saturn ten*), and also
observe one moon ending its month three times in one Martian day. It is
a singular case in the solar system among the natural satellites that
a moon completes one revolution before its primary finishes one rotation.

Swift ascribed to the Laputans some amazing knowledge—actually
he himself displayed, it is claimed, an unusual gift of foreknowledge.
The chorus of wonderment can be heard in the evaluation of C. P. Olivier
in his article “Mars” written for the Encyclopedia Americana (1943):

“When it is noted how very close Swift came to the truth, not only
in merely predicting two small moons but also the salient features of
their orbits, there seems little doubt that this is the most astounding
’prophecy’ of the past thousand years as to whose full authenticity
there is not a shadow of doubt.”

The passage in Kepler is little known—Olivier, like other writers on
the subject of Swift’s divination, was unaware of it, and the case of
Swift’s prophecy appears astounding: the number of satellites, their close
distances to the body of the planet, and their swift revolutions are stated
in a book printed one hundred and fifty years to the year before the discovery
of Asaph Hall.

Let us examine the case. Swift, being an ecclesiastical dignitary and
a scholar, not just a satirist, could have learned of Kepler’s passage
about two satellites of Mars; he could also have learned of them in Homer
and Virgil where they are described in poetic language (actually, Asaph
Hall named the discovered satellites by the very names the flaming trabants
of Mars were known by from Homer and Virgil); and it is also not inconceivable
that Swift learned of them in some old manuscript dating from the Middle
Ages and relating some ancient knowledge from Arabian, or Persian, or
Hindu, or Chinese sources. To this day an enormous number of medieval
manuscripts have not seen publication and in the days of Newton (Swift
published Gulliver’s Travels in the year Newton was to die), as
we know from Newton’s own studies in ancient lore, for every published
tome there was a multiplicity of unpublished classical, medieval, and
Renaissance texts.

That Swift knew Kepler’s laws, he himself gave testimony, and this in
the very passage that concerns us: “. . . so that the squares of their
periodical times are very near in the same proportion with the cubes of
their distance from the center of Mars” is the Third Law of Kepler.

But even if we assume that Swift knew nothing apart from the laws of
Kepler to make his guess, how rare would be such a guess of the existence
of two Martian satellites and of their short orbits and periods? As to
their number, in 1726 there were known to exist: five satellites of Saturn,
four of Jupiter, one of Earth, and none of Venus. Guessing, one could
reasonably say: none, one, two, three, four, or five. The chance of hitting
on the right Figure was one in six, or the chance of any one side of a
die’s coming up in a throw. The smallness of the guessed satellites would
necessarily follow from their not having been discovered in the age of
Newton. Their proximity to the parent planet and their short periods of
revolution were but one guess, not two, by anybody who knew of the work
of Newton and Kepler. The nearness of the satellites to the primary could
have been assumed on the basis of what was known about the satellites
of Jupiter and Saturn, lo, one of the Galilean (or Medicean) satellites
of Jupiter, revolves around the giant planet in I day 18.5 hours (the
satellite closest to Jupiter was discovered in 1892 by Barnard and is
known as the “fifth satellite” in order of discovery; it revolves around
Jupiter, a planet ten thousand times the size of Mars, in 1 1.9 hours).
The three satellites of Saturn discovered by Cassini before the days of
Swift - Tethys, Dione and Rhea - revolve respectively in I day 21.3 hours,
2 days 17 hours, and 4 days 12.4 hours. (Mimas and Enceladus, discovered
by Herschelin 1789, revolve in 22. 6 hours and I day 8.9 hours.) The far
removed satellites of Jupiter were not yet discovered in the days of Newton
and Swift.

It remains to compare the figures of Swift with those of Hall: there
was no true agreement between what the former wrote in his novel and what
the latter found through his telescope. For Deimos, Swift’s figure, expressed
in miles from the surface of Mars, is 18,900 miles; actually it is 12,500
miles; Swift gave its revolution time as 21.5 hours—actually it is 30.3
hours. For Phobos, Swift’s figures are 10,500 miles from the surface and
10 hours revolution period, whereas the true Figures are 3,700 miles and
7.65 hours. Remarkable remains the fact that for the inner satellite Swift
assumed a period of revolution, though not what it is, but shorter than
the Martian period of rotation, which is true. However, Swift did not
know the rotational period of Mars and therefore he was not aware of the
uniqueness of his figure. If he were to calculate as an astronomer should,
he would either have decreased the distance separating the inner satellite
from Mars - a distance for which he gave thrice its true value - or increased
its revolution period to comply with the Keplerian laws by assuming the
specific weight of Mars as comparable with that of Earth. But Swift had
no ambitions toward scientific inquiry in his satirical novel.

References

The reference is found in the collected works of Kepler
(Astronomica opera omnia, ed. C. Frisch, vol. VI, p. 557) published
in 1866.